Republican presidential candidate Herman Cain's 9-9-9 tax plan has taken a lot of heat recently. One of the biggest criticisms: several independent analysts have found that under the plan, poor and middle class families would pay higher taxes while the richest of the rich would see a substantial tax cut. Today in Detroit, Cain unveiled his response.

"If you're at or below the poverty level, your plan isn't 9-9-9," said Cain with the abandoned Michigan Central Station in the background. "It's 9-0-9."

As a reminder, Cain's plan would scrap the current tax code and replace it with a nine percent business tax, a nine income tax and a nine percent sales tax. For the poor, Cain says income taxes would be zeroed out. But at least one tax expert says this doesn't solve the problem.

Roberton Williams with the non-partisan Tax Policy Center says even with this change the lowest income Americans would see their tax bills rise because the business tax would trickle down to them and "you would still have the sales tax," says Williams. It would still be "nine percent on every dollar they spend, and for poor families, that's a deal breaker."

The Tax Policy Center released an analysis earlier this week that found 84 percent of families would see their tax burden increase under the Cain plan. Williams says this change likely doesn't affect the outcome.

"A few who currently pay somewhat higher taxes now for various reasons might be better off, but for the most part, we'd still expect to see close to 84 percent of families being made worse off by the Cain plan," says Williams.

For cities, Cain introduced the concept of "Opportunity Zones" — areas where there would be special tax advantages to encourage businesses to hire, though he didn't provide a lot of detail about exactly how it would work or how the zones would be chosen.

"We already had this provision in there and we still raised the same amount of money," he said at the event.

Wait? Is Cain saying he's had a provision for poor people in his 9-9-9 plan all along? Yes, and he says his critics just haven't been reading his plan carefully enough.

Language about the plan on his website has changed over time. But, as of this writing, it doesn't say anything about people at or below the poverty line, and neither does his new brochure about the Opportunity Zones. An analysis of the plan commissioned by the Cain campaign and posted on its website says the following:

Relief for lower income taxpayers will inevitably be part of any tax reform. To illustrate the effect that progressivity could have on tax rates, we will later derive the rates needed to allow a refundable exemption equal to the poverty level of income. This is the same as a refundable credit equal to the tax rate times the poverty level of income. This simplifies the estimation as the aggregate poverty amount is just subtracted from the gross tax base for each proposal.

Last week, I interviewed Gary Robbins of Fiscal Associates who did the analysis. When he did his calculations, he figured that there would be a poverty grant of some kind so that "no one in poverty would actually owe any tax."

I asked him if that was part of the Cain plan. His response: "I don't know...this is sort of hypothetical on my part because I don't know how they're going to structure it."

The tax break for those in poverty outlined by the campaign today, is far smaller than what Robbins had calculated. It's not clear whether the Opportunity Zones make up the difference or whether they were in the plan all along. The description of 9-9-9 on Cain's website mentions only Empowerment Zones, not Opportunity Zones.